In the figure below, segment AC is congruent to segment AB:

Which statement is used to prove that angle ABD is congruent to angle ACD?
Triangle ACD is similar to triangle ABD.
Triangle ACD is congruent to triangle ABD.
Segment AD is congruent to segment AC.
Segment AD is congruent to segment DC.

we are given two system of equations

First equation is

[tex]y=2x-1[/tex]

we can write as

[tex]-2x+y=-1[/tex]

Second equation is

[tex]6x-y=13[/tex]

now, we can find augmented matrix

[tex]A=\begin{pmatrix}-2&1&-1\\ 6&-1&13\end{pmatrix}[/tex]

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by -1/2

[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 6&-1&13\end{pmatrix}[/tex]

step-2: add -6 times the 1st row to the 2nd row

[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 0&2&10\end{pmatrix}[/tex]

step-3:multiply the 2nd row by 1/2

[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 0&1&5\end{pmatrix}[/tex]

step-4:add 1/2 times the 2nd row to the 1st row

[tex]A=\begin{pmatrix}1&0&3\\ 0&1&5\end{pmatrix}[/tex]

so, we will get

[tex]x=3,y=5[/tex]

Answer is (3,5)

Answer:

B.y=−3x−1

Step-by-step explanation:

given that the line is parallel to y = -3x+4

Hence required line will be of the form

y =-3x+k for some k.

(Reason: slopes will be equal for parallel lines)

Since the line passes through (-2,5)

Substitute x =-2 and y =5 in the equation.

5=-3(-2)+k

Simplify

5 = 6+k

Subtract 6

Or k =-1

Hence required line has equation y =-3x-1

Let's have time in minutes as x.

Now we will make the next equation

3x+126 = 2x+151  First we will add number (-126) to the both sides and get

3x+126-126=2x+151-126 => 3x= 2x + 25

3x=2x+25 Now we will add monom (-2x) to the both sides and get

3x-2x=2x-2x+25 => x=25 minutes

They spent the same time 25 minutes and earned the same amount of money

Wilson earned  3*25+126= 75+126= $201

Jonathan earned 2*25+151=50+151= $201

Good luck!!!

The ball hits the ground at unknown time (t) when the height (h) = 0

h(t) = -16t² + vt + h    ⇒ v = 64, h = 0, h(t) = 0, find t

 0  = -16t² + 64t

 0  = -16t(t - 4)

0 = -16t       or    0 = t - 4

  t = 0         or        t = 4

It starts at t = 0 seconds and ends at t = 4 seconds

Answer: B

Final answer:

Using the kinematic equation for vertical motion, we find that the golf ball will hit the ground after 4 seconds. We factor the kinematic equation to solve for the time given initial velocity and gravity's acceleration, ignoring the 0 time solution. TΔherefore, the correct option is b.

Explanation:

The question asks after how many seconds a golf ball hit from ground level with an initial vertical velocity of 64 ft/s will hit the ground. This problem involves kinematic equations of motion under the influence of gravity. We can use the equation for vertical motion: distance = initial velocity × time + 0.5 × acceleration × time². Since the ball returns to ground level, the distance covered is 0. Taking downward as positive, gravity's acceleration is +32 ft/s² (the usual acceleration due to gravity in units of ft/s²). We can rearrange the equation to solve for time (t): 0 = 64t + 0.5 × 32t². Factoring out t gives us t(64 + 16t) = 0, and solving for t gives us t = 0 or t = -64/16 = -4 seconds. Since time cannot be negative in this context, the positive solution reflects the time after launch, thus the answer is 4 seconds, which is option b.

Answer:

It's false, only if the situation gets worse.

Step-by-step explanation:

On the off chance that a debate over a contract emerges and casual endeavors at determination fall flat, the foremost common next step may be a claim. On the off chance that the sum at issue is underneath a certain dollar figure (ordinarily $3,000 to $7,500 depending on the state), the parties may be able to resolve the issue in small claims court.

Please correct any mistakes in my answer :) Glad to help ya!

The non real roots 1+4i and -4i will also have their complements as roots:- 1 - 4i and 4i

So the least number of roots = 5 and this will also be the least possible degree of the polynomial.

answer 5

Answer:

D

Step-by-step explanation:

$0.07. use the formula provided and just substitute.

Cost per gallon= Price per gallon/miles per gallon.

cost=$2.56/35

That led to 0.0731428571 and the nearest cent would be $0.07

Answer: Two consecutive square numbers be 16 and 9.

Step-by-step explanation:

Let first consecutive square number be x²

Let second consecutive square number be (x+1)²

According to question,

[tex]x^2\times (x+1)^2=144[/tex]

Now we'll do this by factorisation,

[tex]144=2\times2\times2\times2\times3\times3\\\\144=16\times 9[/tex]

So, two consecutive square numbers are 16 and 9

Consecutive numbers are numbers that follow one another.

The consecutive squares are: 9 and 16

Let the bigger square be x^2

So, we have:

[tex]\mathbf{(x - 1)^2 \times x^2 = 144}[/tex]

Express 144 as 12^2

[tex]\mathbf{(x - 1)^2 \times x^2 = 12^2}[/tex]

Take square roots of both sides

[tex]\mathbf{(x - 1)\times x = 12}[/tex]

Expand

[tex]\mathbf{x^2 - x = 12}[/tex]

Rewrite as:

[tex]\mathbf{x^2 - x - 12 = 0}[/tex]

Expand

[tex]\mathbf{x^2 - 4x +3x- 12 = 0}[/tex]

Factorize

[tex]\mathbf{x(x - 4) +3(x- 4) = 0}[/tex]

Factor out x - 4

[tex]\mathbf{(x +3) (x- 4) = 0}[/tex]

Solve for x

x= -3 or x = 4

x cannot be negative.

So: x = 4

Square both sides

[tex]\mathbf{x^2 = 4^2}[/tex]

[tex]\mathbf{x^2 = 16}[/tex]

Calculate the smaller square

[tex]\mathbf{(x - 1)^2 = (4-1)^2}[/tex]

[tex]\mathbf{(x - 1)^2 = 9}[/tex]

Hence, the consecutive squares are: 9 and 16

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the answer is 87.96 your gonna have to trust me I don't have enough time to explain right now.

Answer:

[tex]\text{The equation of line is }x=-4[/tex]      

Step-by-step explanation:

Given that line is passing through the point (-4, 0) and parallel to the y-axis.

we have to find the equation of the line.

[tex]\text{As the slope of y-axis is }\infty\text{ i.e }\frac{1}{0}[/tex]

Since the slope of parallel lines are equal therefore we have to find the equation of line with slope infinity and passing through the point (-4, 0).

The equation of line pass through the point (x',y') with slope m is

[tex]y-y'=m(x-x')[/tex]

The equation of line with slope infinity and passing through the point (-4, 0) is

[tex]y-0=\frac{1}{0}(x-(-4))[/tex]

[tex]x+4=0[/tex]

[tex]x=-4[/tex]

which is required equation.

Hence, option 1 is correct.

Replace x and Y in the answers and see which one works:

A) 4(4) -3 = 16-3 = 13, not -3 FALSE.

B) 1/2(4) - 5 = 2-5 = -3 TRUE

The correct answer is B

The function represented by the graph is (b) the reciprocal, y = 1/x

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that

The function has horizontal and vertical asymptotes

Only rational functions have this property

This means that the function represented by the graph is (b) the reciprocal, y = 1/x

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If the points P, Q and R are collinear, then a slope of line PQ and a slope of line QR are equal.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

PQ → (0, 3), (2, 0).

Substitute:

[tex]m=\dfrac{0-3}{2-0}=\dfrac{-3}{2}=-1.5[/tex]

QR → (2, 0), (4, -3).

Substitute:

[tex]m=\dfrac{-3-0}{4-2}=\dfrac{-3}{2}=-1.5[/tex]

CORRECT :)

Answer:

-3/2

Step-by-step explanation:

I just did this lesson.

The line has a slope of -3/2

The requried simplified value of the given function at x = 1/2 is 5/8.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given function f(x) = -3/4x + 1
For f(1/2), put x = 1/2 in the above expression,

f(1/2) = -3/4(1/2) + 1
f(1/2) = -3/8 + 1
f(1/2) = [-3 + 1×8]/8
f(1/2) = [5]/8
f(1/2) = 5/8

Thus, the requried simplified value of the given function at x = 1/2 is 5/8.

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Answer: the first choice, |x − 18.25| > 0.36; x < 17.89 or x > 18.61

Explanation:

1. Target weight: 18.25 oz

2. Variability accepted: 0.36 oz

3. Range of accepted masses: 18.25 oz - 0.36 oz ≤ x ≤ 18.25 oz + 0.36 oz

4. Addition property of the inequalities (subtract 18.25 oz to the three parts of the inequality):

- 0.36 oz ≤ x - 18.25 oz ≤ 0.36 oz

5. Definition of absolute value inequality: | x - a | ≤ c equals - c ≤ x - a ≤ c

   ∴ - 0.36 ≤ x - 18.25 ≤ 0.36  equals | x - 18.25 | ≤ 0.36, which is the range of accepted masses.

6. The range of rejected masses is the complement, so it is:

          |x - 18.25 | > 0.36

7. Solve the inequality to find the range of rejected masses:

    a) x - 18.25 > 0.36 ⇒ x > 18.25 + 0.36 ⇒ x > 18.61

    b) x - 18.25 < 0.36 ⇒ x < 18.25 - 0.36 ⇒ x < 17.89

-58.82% is the percent increase

Answer:

1/4 = 3/12 and 1/6 = 2/12

Step-by-step explanation:

We are given two fractions with denominator 4 and 6.

To find the least common denominator, of 4 and 6.

Factorise 4 and 6.

4 = 2x2

6=2x3

Hence Least common denominator = 2x2x3 =12

Make the given fractions to equivalent fractions with common denominator 12.

1/4 = 1(3)/4(3) = 3/12 and

1/6 = 1(2)/6(2)= 2/12

Hence answer would be

3/12 and 2/12

To rewrite the fractions 1/4 and 5/6 with a least common denominator, find the least common multiple (LCM) of the denominators, which is 12. Multiply the numerators and denominators of each fraction by the appropriate factor to obtain the rewritten fractions.

To rewrite the fractions 1/4 and 5/6 with a least common denominator, we need to find the least common multiple (LCM) of the denominators, which in this case are 4 and 6.

To find the LCM, we can list the multiples of each denominator until we find a common multiple. For 4, the multiples are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... And for 6, the multiples are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... The first common multiple we find is 12, so that is the least common denominator (LCD).

To rewrite 1/4 with the LCD of 12, we need to multiply both the numerator and the denominator by 3: (1 * 3) / (4 * 3) = 3/12.

To rewrite 5/6 with the LCD of 12, we need to multiply both the numerator and the denominator by 2: (5 * 2) / (6 * 2) = 10/12.

Answer:

  $5.99

Step-by-step explanation:

Purchase amounts are rounded to the penny.

(3/4 lb)×$7.99/lb = $5.9925 ≈ $5.99

11-7=4

7*4=28

28is your answer

16/13/4=

64/13

4and12/13

From a 16 foot board, 4 full pieces each 3 1/4 feet long can be cut. Moreover, 16.0 inches, a common spacing for vertical studs, is equivalent to 40.64 centimeters.

To determine how many lengths of 3 1/4 feet can be cut from a 16 foot board, we need to divide the total length of the board by the length of each desired piece. First, we convert the mixed number 3 1/4 to an improper fraction, 13/4. Then, we perform the division: 16 feet divided by 13/4 feet.

This calculation can be set up as follows:

(16 feet) \/ (13/4 feet) = (16 feet) × (4/13) = (64/13) feet = 4 remainder 12/13

Therefore, you can cut 4 full pieces that are 3 1/4 feet long from a 16 foot board, with a remainder of 12/13 of a foot.

If we want to convert the placement of vertical studs, which are typically 16 inches apart, to centimeters, we use the conversion factor that 1 inch equals 2.54 centimeters. 16.0 inches multiplied by 2.54 equals 40.64 centimeters.

3,744 inches. You would multiply 312 and 12, since there is 12 inches in a foot, to get 3,744 inches.

Hope this helped! :)

Given : AB = 44 + 3x

BC = 33 + x

CD = 64 − x

AD = 48 − 2x.

Opposite sides are AB and CD.

BC and AD.

Setting AB equals CD

We get

44 + 3x = 64 − x

Adding x on both sides, we get

44 + 3x+x = 64 − x+x

44 +4x = 64.

Subtracting 44 from both sides, we get

44-44 +4x = 64 - 44.

4x =20

Dividing both sides by 4, we get

x= 5.

Let us plug x=5 to find the length of each side, we get

AB = 44 + 3x = 44 +3(5) = 44 + 15 = 59 cm

BC = 33 + x = 33 + 5 = 38 cm

CD = 64 − x = 64 - 5 = 59 cm

AD = 48 − 2x = 48 - 2(5) = 48 - 10 = 38 cm.

V=480cm³ . 10 and 12

the first few bars are the people who walked fewer than 4,000, so add up the numbers on the side (2 and 5) and you get 7, so a

7 people have averaged fewer than 4,000 steps.

Option A is the correct answer.

Given,

The bar graph of the number of steps on the horizontal line and the number of people on the vertical line.

We need to find how many people averaged fewer than 4,000 steps each day.

Read the bar graph.

Steps - 0 - 1,999

= 2 people

Steps - 2,000 - 3,999

= 5 people

Steps - 4,000 - 5,999

= 12 people

Steps - 6,000 - 7,999

= 7 people

Steps - 8,000 - 9,999

= 3 people

Find the number of people who have fewer than 4,000 steps.

We have,

Steps - 0 - 1,999

= 2 people

Steps - 2,000 - 3,999

= 5 people

So,

2 + 5 = 7

= 7 people

Thus 7 people have averaged fewer than 4,000 steps.

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the value of x for which L is parallel to M :28 done

Leila's gross earnings are calculated by adding her base pay of $290 to her commission of $13.80, which is 3% of her sales over $500. For the week, her total gross earnings are $303.80.

The question involves calculating Leila's gross earnings for a week where she sold $960 worth of merchandise while working at Famous Footwear. To find her earnings, we need to calculate her base pay plus the commission on sales over $500.

Leila's base pay is $290 per week. Since she sold $960, the amount over $500 that is eligible for commission is $960 - $500 = $460. Her commission is 3% of this amount, which is 0.03 * $460 = $13.80.

Therefore, Leila's total gross earnings for the week are her base pay plus her commission: $290 + $13.80 = $303.80.

Answer:

The correct answer is option D, the approximate population density of the bacteria in the dish is 4,246 bacteria / square inch

Step-by-step explanation:

They give us the diameter of the plate, then the first step is to calculate their area.

The area of a circle according to the diameter is:

[tex]A = \frac{\pi}{4}(d) ^ 2[/tex]

Where d is the diameter.

So:

[tex]A = \frac{\pi}{4}36\\ A = 9\pi\\ A = 28.274.inches ^ 2[/tex]

Now, to find the number of bacteria in per square inch, we divide [tex]\frac{120000}{28.274} = 4244.132.[/tex]

So, the correct answer is option D, the approximate population density of the bacteria in the dish is 4,246 bacteria / square inch